We derive the fundamental plane (FP) relation for a sample of 1430 early-type galaxies in the optical (r band) and the near-infrared (K band), by combining SDSS and UKIDSS data. With such a large, homogeneous data set, we are able to assess the dependence of the FP on the wave band. Our analysis indicates that the FP of luminous early-type galaxies is essentially wave band-independent, with its coefficients increasing at most by 8% from the optical to the NIR. This finding fits well into a consistent picture in which the tilt of the FP is not driven by stellar populations but results from other effects, such as nonhomology. In this framework, the optical and NIR FPs require more massive galaxies to be slightly more metal-rich than less massive ones, and to have highly synchronized ages, with an age variation per decade in mass smaller than a few percent.